Download Applied Probability

Course
Specifications
Valid as from the academic year 2016-2017
Applied Probability (E003110)
Course size
Credits 3.0
(nominal values; actual values may depend on programme)
Study time 90 h
Contact hrs
30.0 h
Course offerings and teaching methods in academic year 2016-2017
A (semester 2)
seminar
15.0 h
lecture
15.0 h
Lecturers in academic year 2016-2017
Wittevrongel, Sabine
TW07
lecturer-in-charge
Offered in the following programmes in 2016-2017
crdts
Bachelor of Science in Computer Science Engineering
3
Bachelor of Science in Electrical Engineering
3
Bridging Programme Master of Science in Industrial Engineering and 3
Operations Research
Bridging Programme Master of Science in Industrial Engineering and 3
Operations Research
Preparatory Course Master of Science in Bioinformatics (main
3
subject Engineering)
Preparatory Course Master of Science in Industrial Engineering and
3
Operations Research
offering
A
A
A
A
A
A
Teaching languages
Dutch
Keywords
Probability theory, random variables, distributions, entropy, random processes,
stochastic signals
Position of the course
The course aims at the introduction and practical use of the principal concepts and
properties from probability theory that are required for the stochastic modelling of
(engineering) systems. Specifically, the course discusses concepts and properties from
probability theory, basic concepts and properties from information theory, properties of
various types of stochastic processes (such as birth-death processes, Poisson
processes, Markov chains and renewal processes) and basic concepts w.r.t. stochastic
signals. The course builds upon the bachelor courses Probability and Statistics and
Analysis of systems and signals and gives a mathematical, theoretical basis for various
other courses of a more applied nature such as Communication Theory, Information
Theory and Queueing Theory.
Contents
• Probability theory: Random variables and their distributions, Functions of random
• variables, Laplace transform of the density of a continuous random variable,
• Probability generating function of a discrete random variable, Inequalities and limit
• theorems
• Uncertainty and entropy: Entropy of a discrete random variable, Principle of
• maximum entropy
• Random processes: Definition, Basic properties, Classification
• Point processes: Birth-death processes, Poisson processes, Renewal processes,
• Markov chains
• Stochastic signals: Stationarity, Ergodicity, Correlation functions, Energy and power
• spectra, Filtered signals
Initial competences
(Approved)
1
Basic probability theory (see e.g. course 'Probability and Statistics'); z transform,
Laplace transform, basic knowledge signals (see e.g. course 'Analysis of Systems and
Signals').
Final competences
1 To determine distributions of (functions of) random variables.
2 To calculate and to interpret characteristics of random variables as moments and
1 entropies.
3 To understand and to apply the properties of random processes such as birth-death
1 processes, Poisson processes, renewal processes and Markov chains.
4 To analyse the time-dependent and limiting behavior of random processes.
5 To calculate and to interpret characteristics of random processes and stochastic
1 signals.
Conditions for credit contract
Access to this course unit via a credit contract is determined after successful competences
assessment
Conditions for exam contract
This course unit cannot be taken via an exam contract
Teaching methods
Lecture, seminar
Learning materials and price
Dutch syllabus (about 10 euro); additional course material (available via Minerva).
References
• A. Leon-Garcia: "Probability, Statistics, and Random Processes for Electrical
• Engineering", Pearson Education, 2009.
• A. Papoulis, S.U. Pillai: "Probability, Random Variables and Stochastic Processes",
• McGraw-Hill, 2002.
Course content-related study coaching
By the lecturer and assistants: contacts are possible during or after the lectures and
problem solving sessions, by means of email or after making an appointment.
Evaluation methods
end-of-term evaluation
Examination methods in case of periodic evaluation during the first examination period
Open book examination
Examination methods in case of periodic evaluation during the second examination period
Open book examination
Examination methods in case of permanent evaluation
Possibilities of retake in case of permanent evaluation
not applicable
Extra information on the examination methods
Written open-book exam (only syllabus)
Calculation of the examination mark
(Approved)
2